After observing the defects within individual candies in man

After observing the defects within individual candies in many bags of M&Ms, it has been determined that 11% of all candies are defective, that the probability of observing an M&M with a missing letter is 22%, and the probability of observing a cracked M&M given that you already know it is defective is 70%. What is the probability that you randomly select an M&M that is cracked?

a. 0

b. 0.077

c. 0.700

d. 0.770

Solution

P( defective) = 0.11
P( Missing Letter) = 22% of 11 = 0.0242
P( Cracked | Defective) = 0.70

P( Cracked | Defective) = P( Cracked & Defective) / P(Defective)
0.70 = P( Cracked & Defective) / 0.11

P( Cracked & Defective) = 0.70 * 0.11 = 0.077